{
  "id": "0906.2889",
  "version": "v3",
  "published": "2009-06-16T14:57:27.000Z",
  "updated": "2011-04-28T16:41:45.000Z",
  "title": "Normal curvature bounds along the mean curvature flow",
  "authors": [
    "Hong Huang"
  ],
  "comment": "4 pages, some corrections",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Let $(M^n,g_0)$ and $(\\bar{M}^{n+1},\\bar{g})$ be complete Riemannian manifolds with $|\\bar{\\nabla}^k\\bar{Rm}|\\le \\bar{C}$ for $k \\le 2$, and suppose there is an isometric immersion $F_0: M^n \\rightarrow \\bar{M}^{n+1}$ with bounded second fundamental form. Let $F_t: M^n \\rightarrow \\bar{M}^{n+1}$ ($t\\in [0,T]$) be a family of immersions evolving by mean curvature flow with initial data $F_0$ and with uniformly bounded second fundamental forms. We show that the supremum and infimum of the normal curvature of the immersions $F_t$ vary at a bounded rate. This is an analogue of a result of Rong and Kapovitch on Ricci flow.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-04-28T16:41:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "mean curvature flow",
      "normal curvature bounds",
      "uniformly bounded second fundamental forms",
      "complete riemannian manifolds",
      "initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2889H"
    }
  }
}